Green’s Equivalence Classes in Full Transformation Semigroups: A Height-based Approach
Date
2025-04-12
Authors
Usamot Foluke Idayat, Ibrahim Garba Risqot, Bakare Gatta Naimat, Adeshola Adediran Dauda , Aliu Tajudeen Olaniyi
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematics, Universitas Negeri Gorontalo, Indonesia
Abstract
Green’s relations constitute five distinct equivalence classes that serve to define the elements of a semi-
group. In this work, the equivalence classes within the Full Transformation Semigroup (Tκ) were systematically enu-
merated according to their respective heights, and the findings derived were subsequently generalized through the
application of a combinatorial assertion and their graphical representations included to substantiate the theoretical
results.